Tunable diode laser absorption spectroscopy tomography (TDLAT) is an important optical noninvasive combustion detection technique. Two-line thermometry is widely used in TDLAT for temperature imaging, in which the absorbance density distributions for two spectral transitions with different temperature-dependent line strengths are individually reconstructed, and the temperature image is then retrieved from the ratio of the absorbances in each pixel of the region of interest. Owing to the limited number of available line-of-sight TDLAT measurements in practical applications, the inverse problem of reconstructing the absorbance density distribution is inherently ill-posed, leading to severe artifacts in the reconstructed temperature image. To alleviate this problem, iterative tomographic algorithms have been proposed by formulating an inverse problem with a heuristically determined prior, such as the smoothness of absorbance density distributions. These algorithms improve the quality of the reconstructed smooth characteristics in temperature images to some degree; however, the lack of detailed features in the reconstructed image is evident. To address this problem, a cartoon-texture model in the field of image processing is introduced into TDLAT, and the temperature reconstruction algorithm based on the cartoon-texture model (TRACT) is proposed.
The proposed TRACT individually reconstructs the cartoon and textural components of the absorbance density distribution with smoothness and sparsity priors, and retrieves the temperature image with two-line thermometry from the combination of the reconstructed cartoon and texture components. First, the cartoon component is reconstructed using the total variation (TV) regularized Landweber algorithm (Landweber-TV) to effectively retrieve the smooth characteristics and edge structure in the absorbance density distribution. Second, the texture component is reconstructed with a modified deep network unfolded using the iterative shrinkage-thresholding algorithm (ISTA-mNet) to supplement the detailed information in the absorbance density distribution. Third, the temperature image is reconstructed using two-line thermometry from the complementation of cartoon-component and texture-component reconstructions of the absorbance density distribution. With complementary reconstructions of the cartoon and texture components, the accuracy of the retrieved absorbance density distribution and the quality of the reconstructed temperature image are improved.
To examine the performance of the proposed TRACT, it is compared with two state-of-the-art iterative tomographic algorithms and one pioneering data-driven tomographic algorithm for TDLAT temperature imaging. These are temperature imaging algorithms based on Landweber (referred to as Landweber), algebraic reconstruction techniques and TV regularization (referred to as ART-TV), and convolutional neural networks (referred to as HCNN). In addition, to verify the effectiveness of the cartoon-texture model, TRACT is compared to the temperature imaging algorithm based on Landweber-TV, that is, the cartoon-component reconstruction algorithm. In the simulations, the dataset is generated using Fire Dynamic Simulator (FDS). Tests are conducted in a practical signal-to-noise ratio (SNR) range of 25 dB?45 dB. The normalized mean square error (NMSE) is adopted to quantitatively evaluate the reconstruction accuracy. The simulation results show that the NMSE obtained by TRACT is always lower than those obtained by the other four algorithms (Fig. 5). Taking an SNR of 35 dB as an example, compared with the NMSEs obtained by Landweber, ART-TV, HCNN, and Landweber-TV, the NMSE obtained by TRACT decreases by 58.67%, 51.96%, 39.44%, and 35.38%, respectively. In terms of subjective quality, the temperature image reconstructed by TRACT is more consistent with the ground-truth phantom, and less information remained in the residual image than in the temperature images reconstructed by Landweber, ART-TV, HCNN, and Landweber-TV (Fig. 6). Laboratory-scale experiments are conducted to validate the performance of the proposed TRACT. In the temperature image reconstructed by TRACT from the actual TDLAT measurements, the location of the flame agrees better with the true combustion field, and fewer artifacts exist compared to the temperature images reconstructed by Landweber, ART-TV, HCNN, and Landweber-TV (Fig. 7). Moreover, the peak temperature value retrieved by TRACT is closer to the highest temperature value measured by the thermocouple than those retrieved by the other four algorithms.
The cartoon-texture model is introduced into the TDLAT, and a temperature reconstruction algorithm based on the cartoon-texture model (TRACT) is proposed. TRACT utilizes the Landweber-TV iterative tomographic algorithm and the ISTA-mNet network, designed with different priors of the image features, to achieve efficient reconstruction of the cartoon and detailed texture components in the absorbance density distribution, respectively. This improves the accuracy of the reconstructed absorbance density distributions and, in turn, the quality of the reconstructed temperature image. Simulations with the dataset generated from the fire dynamics simulator showed that, in comparison to Landweber, ART-TV, HCNN, and Landweber-TV, the normalized mean square errors obtained by TRACT decrease by 54.37%?58.67%, 45.93%?51.96%, 29.60%?39.44%, and 28.48%?35.38%, respectively, in the SNR range of 25 dB?45 dB. The temperature images reconstructed by TRACT have fewer artifacts and are closer to the ground-truth phantoms. Reconstructions with actual TDLAT measurements obtained from the lab-scale TDLAT system show that in comparison to Landweber, ART-TV, HCNN, and Landweber-TV, the performance of TRACT for reconstructing the temperature distribution in a real combustion field is higher, as evaluated quantitatively and visually.
